Advertisement

Three-Dimensional Formulation of the Relativistic Two-Body Problem

  • V. G. Kadyshevskii
  • R. M. Mir-Kasimov
  • N. B. Skachkov

Abstract

A quasipotential approach to the relativistic two-body problem is developed on the basis of the three-dimensional Hamiltonian formulation of quantum field theory. A relativistic configuration representation is introduced and studied on the basis of a decomposition with respect to matrix elements of irreducible unitary representations of the Lorentz group. A representation is obtained for the quasipotential scattering amplitude at high energies that generalizes the nonrelativistic eikonal formula.

Keywords

Recursion Relation Lorentz Group Relativistic Particle Schrodinger Equation Nonrelativistic Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    J. Schwinger, Proc. Nat. Acad. Sci. USA, 37, 452 (1951).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    E. Salpeter and H. Bethe, Phys. Rev., 54, 1232 (1951).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    M. Gell-Mann and F. Low, Phys. Rev., 84, 350 (1951).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    V. A. Fock, Phys. Assoc. Sowjetunion, 6, 425 (1934).MATHGoogle Scholar
  5. 5.
    I. E. Tamm, Phys. USSR, 9, 449 (1945).Google Scholar
  6. 6.
    S. M. Dancoff, Phys. Rev., 78, 382 (1950).ADSMATHCrossRefGoogle Scholar
  7. 7.
    A. A. Logunov and A. N. Tavkhelidze, Nuovo Cimento, 29, 380 (1963).MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. A. Logunov et al., Nuovo Cimento, 30, 134 (1963).MathSciNetCrossRefGoogle Scholar
  9. 9.
    A. A. Logunov, A. N. Tavkhelidze, and O. A. Khrustalev, Phys. Lett., 4, 325 (1963).MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    B. A. Arbuzov et al., Zh. Éksp. Teor. Fiz., 44, 1409 (1963).Google Scholar
  11. 11.
    A. N. Tavkhelidze, Lectures on the Quasipotential Method in Field Theory, Bombay, Tata Institute of Fundamental Research (1964).Google Scholar
  12. 12.
    V. G. Kadyshevskii and A. N. Tavkhelidze, in: Problems of Theoretical Physics [in Russian] (Dedicated to N. N. Bogolyubov on the occasion of this 60th birthday), Nauka (1969) ([ii, 12] contain detailed bibliographies).Google Scholar
  13. 13.
    V. A. Matveev, R. M. Muradyan, and A. N. Tavkhelidze, Preprint JINR E-3498 [in English], Dubna [see also: C. Fronsdal and L. E. Lundberg, Phys. Rev., 3, 3447 (1970)].Google Scholar
  14. 14.
    V. G. Kadyshevsky (Kadyshevskii), Nucl. Phys., B6, 125 (1968).ADSCrossRefGoogle Scholar
  15. 15.
    V. G. Kadyshevsky (Kadyshevskii) and M. D. Mteev, Nuovo Cimento, 55A, 275 (1967).ADSGoogle Scholar
  16. 16.
    V. G. Kadyshevskii, Zh. Éksp. Teor. Fiz., 46, 654 (1964).Google Scholar
  17. 17.
    V. G. Kadyshevskii, Zh. Éksp. Teor. Fiz., 46, 872 (1964).Google Scholar
  18. 18.
    V. G. Kadyshevskii, Dokl. Akad. Nauk SSSR, 160, 573 (1965)MathSciNetGoogle Scholar
  19. 19.
    V. G. Kadyshevsky (Kadyshevskii), R. M. Mir-Kasimov, and N. B. Skachkov, Nuovo Cimento, 55A, 233 (1968).ADSCrossRefGoogle Scholar
  20. 20.
    V. G. Kadyshevskii, R. M. Mir-Kasimov, and N. B. Skachkov, Yad. Fiz., 9, 219 (1969).Google Scholar
  21. 21.
    V. G. Kadyshevskii, R. M. Mir-Kasimov, and N. B. Skachkov, Yad. Fiz., 9, 462 (1969).Google Scholar
  22. 22.
    V. G. Kadyshevskii, R. M. Mir-Kasimov, and M. Freeman, Yad. Fiz., 9, 646 (1969).Google Scholar
  23. 23.
    V. G. Kadyshevskii, M. D. Mateev, and R. M. Mir-Kasimov, Yad. Fiz., 11, 692 (1970).Google Scholar
  24. 24.
    M. Freeman, M. D. Mateev, and R. M. Mir-Kasimov, Nucl. Phys., B12, 197 (1969).ADSCrossRefGoogle Scholar
  25. 25.
    A. S. Wightman, Lectures on Invariance in Relativistic Quantum Mechanics (les Houches, 1960); in: Dispersion Relations and Elementary Particles, Paris (1960);Google Scholar
  26. I. M. Namislovskii, Phys. Rev., 160, 1522 (1967).ADSCrossRefGoogle Scholar
  27. 26.
    H. Shyder, Phys. Rev., 71, 38 (1947).ADSCrossRefGoogle Scholar
  28. 27.
    Yu. A. Gol’fand, Zh. Éksp. Teor. Fiz., 37, 504 (1954);Google Scholar
  29. Yu. A. Gol’fand, Zh. Éksp. Teor. Fiz., 43, 256 (1962);Google Scholar
  30. Yu. A. Gol’fand, Zh. Éksp. Teor. Fiz., 44, 1248 (1963).Google Scholar
  31. 28.
    V. G. Kadyshevskii, Zh. Éksp. Teor. Fiz., 41, 1885 (1961).Google Scholar
  32. 29.
    I. E. Tamm, in: Proc. 12th International Conference on High-Energy Physics [in Russian], Vol. I I, Moscow, Atomizdat (1964).Google Scholar
  33. 30.
    R. M. Mir-Kasimov, Zh. Éksp. Teor. Fiz., 52, 533 (1967).Google Scholar
  34. 31.
    V. G. Kadyshevskii, Dokl. Akad. Nauk SSSR, 147, 588 (1962).Google Scholar
  35. 32.
    M. A. Naimark, Linear Representations of the Lorentz Group, Pergamon Press, London (1964).Google Scholar
  36. 33.
    I. S. Shapiro, Dokl. Akad. Nauk SSSR, 106, 647 (1956);MATHGoogle Scholar
  37. I. S. Shapiro, Zh. Éksp. Teor. Fiz., 43, 1727 (1962).Google Scholar
  38. 34.
    N. Ya. Vilenkin, Special Functions and the Theory of Group Representations, AMS Translations of Math. Monogr., Vol. 22, Providence, R. I. (1968).Google Scholar
  39. 35.
    A. O. Gel’fond, Calculus of Finite Differences [in Russian], Fizmatgiz, Moscow (1967).Google Scholar
  40. 36.
    L. Brown et al., Ann. Phys., 23, 187 (1963).ADSCrossRefGoogle Scholar
  41. 37.
    E. Fermi and C. N. Yang, Phys. Rev., 76, 1739 (1949).ADSMATHCrossRefGoogle Scholar
  42. 38.
    N. N. Bogolyubov, B. V. Struminskii, and A. N. Tavkhelidze, Preprint JINR D-1968 [in Russian], Dubna (1965).Google Scholar
  43. 39.
    A. N. Tavkhelidze, High-Energy Physics and Elementary Particles, IAEA, Vienna (1965),P. 753.Google Scholar
  44. 40.
    V. R. Garsevanishvili et al., Teor. Mat. Fiz., 7, 203 (1971).Google Scholar
  45. 41.
    R. J. Glauber, Lectures in Theoretical Physics, Vol. 1, Interscience, New York (1959).Google Scholar
  46. 42.
    V. R. Garsevanishvili et al., Phys. Lett., 29B, 191 (1969).Google Scholar
  47. 43.
    V. R. Garsevanishvili et al., Preprint IC/ 69/ 87, Trieste (1969).Google Scholar
  48. 44.
    V. R. Garsevanshvili, V. A. Matveev, and L. A. Slepchenko, in: Particles and Nuclei, Vol. 1, No. 1, Consultants Bureau, New York (1972).Google Scholar

Copyright information

© Consultants Bureau 1973

Authors and Affiliations

  • V. G. Kadyshevskii
  • R. M. Mir-Kasimov
  • N. B. Skachkov

There are no affiliations available

Personalised recommendations